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How to Figure Out the Domain of a Function With a Radical as the Denominator

A function is a mathematical relationship where an "x" value produces one, and only one, value of "y." A rational expression is a fraction that has a variable in the denominator. When a function includes a rational expression, the domain needs to be specified. The domain specifies what values "x" can't equal or it will cause the denominator to equal 0, which isn't allowed mathematically. If the variable in the denominator is under a radical, there are additional rules pertaining to the domain.

Instructions

- 1
  Determine the domain of a function with a radical in the denominator by first creating an equation setting the denominator equal to 0 and solving for the variable. Define the variable further using inequality symbols based on the following rules for radicals: An even root (such as a square root) can't have a negative number under it; an odd root (such as a cube root) can have a negative number.
- 2
  Define the domain of the function f(x) = 3x + 5 / √(x + 2). Set the denominator equal to zero, √(x + 2) = 0. Square both sides of the equation to remove the radical: x + 2 = 0. Subtract 2 from both sides: x = -2.
- 3
  Rewrite the domain in terms of an inequality that will prevent the denominator from equaling a negative number, which isn't allowed under an even radical. Writing x > 2 ensures the answer will remain above 0.

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